Solve the Rational Equation: Isolate X in 5/(x-8) = 3/4x

Solve for X:

5x−8=34x \frac{5}{x-8}=\frac{3}{4x}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We want to isolate the unknown X
00:07 Let's multiply by both denominators to eliminate fractions
00:14 Let's properly open parentheses, multiply by each factor
00:20 Let's arrange the equation so that one side has only the unknown X
00:29 Let's isolate the unknown X
00:35 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

5x−8=34x \frac{5}{x-8}=\frac{3}{4x}

2

Step-by-step solution

To solve the equation 5x−8=34x \frac{5}{x-8} = \frac{3}{4x} for the variable x x , we will follow these steps:

Step 1: Apply cross-multiplication to the equation. This involves multiplying the numerator of each fraction by the denominator of the other fraction:

5⋅4x=3⋅(x−8) 5 \cdot 4x = 3 \cdot (x - 8)

Step 2: Simplify both sides of the resulting equation:

20x=3x−24 20x = 3x - 24

Step 3: Rearrange the equation to isolate terms involving x x on one side:

20x−3x=−24 20x - 3x = -24

This simplifies to:

17x=−24 17x = -24

Step 4: Solve for x x by dividing both sides of the equation by 17:

x=−2417 x = \frac{-24}{17}

Therefore, the solution to the equation is:

x=−2417 x = \frac{-24}{17}

3

Final Answer

−2417 \frac{-24}{17}

Practice Quiz

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Solve for X:

\( 5x=25 \)

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